- #1
ghostfolk
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Homework Statement
A charge distribution is given by ##\rho(r,\theta,phi)=\gamma r^3cos\theta,a<r,b,0\leq\theta\leq\pi/2## and is zero everywhere else. The distance from the origin ##r=\sqrt{x^2+y^2+z^2}## and ##\gamma## is a constant. Write out the electric field P along the z-axis a distance z from the origin as an integral over the charge density. Be sure to include all the limits of integration. Simplify the expression and carry out the ##\phi'## integration, but leave the ##r'## and ##\theta'## integrations.
Homework Equations
##dE=kdq/r^2##
##\rho=Q/V##
The Attempt at a Solution
##dq=\rho dV=\rho2\pi(b-r)^2dr##
So then, ##dE_z=k\frac{\gamma r^3cos\theta(b-r)^2dr}{(z-(b-r))^2}##
Is that the correct way to set up the integral? Any help is appreciated.